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Standard Equation of a Circle

The standard equation of a circle with center (h,k) and radius r is (x-h)²+(y-k)²=r²

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Arc Addition Postulate

The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs

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In a plane, a line is tangent to a circle IFF

the line is perpendicular to a radius of the circle at its endpoint on the circle

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Tangent segments from a common external point are

congruent

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In the same circle, or in congruent circles, two minor arcs are congruent IFF

their corresponding chords are congruent

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If one chord is the perpendicular bisector of another chord

then the first chord is a diameter

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If a diameter of a circle is perpendicular to chord,

then the diameter bisects the chord and its arc

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In the same circle, or in congruent circles, two chords are congruent IFF

they are equidistant from the center

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Measure of an Inscribed Angle Theorem

The measure of an inscribed angle is one half the measure of its intercepted arc

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If two inscribed angles of a circle intercept the same arc,

then the angles are congruent

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An angle inscribed in a semicircle

is a right angle.

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The opposite sides of a quadrilateral inscribed in a circle are

supplementary

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If a tangent and a chord intersect at a point on a circle,

then the measure of each angle formed is one half the measure of its intercepted arc

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